The ASA Rule
Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 23 of 63.
Lay down a side, then draw the two angles at its ends. The two new arms can only cross at one point, so the triangle is fixed. This is ASA, angle side angle: two pairs of equal angles and the equal sides between them.
| Statement | Reason |
|---|---|
| 1. ∠ABC = ∠DEF | Given |
| 2. BC = EF | Given |
| 3. ∠BCA = ∠EFD | Given |
| 4. △ABC ≅ △DEF | ASA, using lines 1, 2 and 3 |
As with SAS, the middle letter is in the middle on purpose. The side must be the included side of the two angles: here BC joins B and C, the two marked corners.
Challenge
The marks show ∠R = ∠X, ∠S = ∠Y, and RS = XY. Prove that △RST ≅ △XYZ, then press Check.
Try it yourself
Write the proof
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Congruence & Proof
1What a Proof Is
Given and ProveStatements and ReasonsChaining Equal PartsYour First Full ProofRecap: A Chain of Reasons2Congruent Triangles
Same Size, Same ShapeMatching SidesMatching AnglesWhat Congruence GivesRecap: Matching Parts8Proofs with Vertical Angles
Vertical Angles in ProofsThe BowtieBowtie with ASALinear Pairs in ProofsRecap: Vertical Angles